This section is intended to provide a background or context to the invention that is recited in the claims. The description herein may include concepts that could be pursued, but are not necessarily ones that have been previously conceived or pursued. Therefore, unless otherwise indicated herein, what is described in this section is not prior art to the description and claims in this application and is not admitted to be prior art by inclusion in this section.
The following abbreviations that may be found in the specification and/or the drawing figures are defined as follows:
CDcritical dimensionDOEdiffractive optical elementDOFdepth of focusEDexposure-defocusIC integrated circuitLPlinear programmingMILPmixed integer linear programming problemMINLPmixed integer nonlinear programming problemMIPmixed integer programming problemMTFmodulation transfer functionOPCoptical proximity correctionRETresolution enhancement techniqueSMOsource mask optimizationSRAM static random access memoryUVultraviolet
Introduction
There is increasing interest in methods to optimize the illumination distributions (referred to as sources) used in photolithography. Future generations of lithographic technology will rely heavily on intensively customized sources to increase the quality of the printing process. Intensively customized sources can be physically realized by using, for example, diffractive optical elements (DOEs).
One prerequisite for satisfactorily exploiting such technology is a method for determining a source distribution that provides a specialized benefit to the lithographic application at hand; such methods are referred to as source optimization methods. Rather than choosing the source using assessments that are purely heuristic, the source may be optimized globally, e.g., by finding the optimum source shape without assuming a starting design, and doing so in a way that maximizes a bona fide lithographic metric. The objective function (merit function) may be configured for obtaining the largest possible exposure latitude in focus, e.g., attaining the sharpest possible focused image. See further: A. E. Rosenbluth, S. Bukofsky, C. Fonseca, M. Hibbs, K. Lai, A. Molless, R. N. Singh, and A. K. Wong, “Optimum Mask and Source Patterns to Print a Given Shape,” JM3 1, no. 1 (2002): p. 13.
Methods exist for extending the approach of “Optimum Mask and Source Patterns to Print a Given Shape” to optimize for maximum possible process window through focus. So-called ED-window analysis (devised many years ago by B. J. Lin and co-workers) provides a convenient framework for assessing lithographic quality in a way that takes both exposure latitude and depth of focus (DOF) into account. The integrated area of the ED-window is in turn a very useful single-parameter metric for assessing overall image quality. Weakest individual window amongst different features can also be optimized, for example under a constraint that the common window be non-negative. See A. E. Rosenbluth and N. Seong, “Global Optimization of the Illumination Distribution to Maximize Integrated Process Window,” SPIE v.6154 Optical Microlithography XIX (2006); [9] A. E. Rosenbluth, “Printing a Mask with Maximum Possible Process Window Through Adjustment of the Source Distribution,” U.S. Pat. No. 7,057,709 (2006); and A. K. Wong, R. Ferguson, S. Mansfield, A. Molless, D. Samuels, R. Schuster, and A. Thomas, “Level-specific lithography optimization for 1-Gb DRAM,” IEEE Transactions on Semiconductor Manufacturing 13, no. 1 (February 2000): p. 76.
The above methods were formulated to maintain (for each individual mask pattern in the set being optimized) an approximately stabilized 2D image cross-section through focus, or through resist depth. A global source solution may be obtained for optimally printing a “3D” image, e.g., a source can be determined that will maximize the integrated range of dose and focus fluctuations (the latter arising, for example, from small variations in the position of the wafer surface relative to the optimal focal plane of the lens) over which the 3D image could successfully be printed. Here “3D” refers to images which are designed to print openings in the film stack whose cross-sections through depth take on a prescribed non-fixed character. An example of this is a dual damascene structure used commonly for metal interconnects in ultra-large scale integrated circuits. It has recently been recognized that fabrication of such resist openings can be carried out more easily if the resist stack is given a varying sensitivity through depth, for example by stacking multiple resist films with different sensitivities. See D. O. S. Melville, A. E. Rosenbluth, and K. Tian, “Method for Printing with Maximum Possible Process Window a Three-dimensional Design through Adjustment of the Source Distribution with Physical Power Constraints,” U.S. Patent Application Publication No. 2009/0021718-A1 (2009).
Limitations of the Conventional Methods for Global Source Optimization
Optimization for maximum process window has been achieved previously through mathematical transformation of percentage dose latitude requirements, to arrive at a reformulation as a near-linear-programming problem—This reformulated problem uses variables representing a scaled version of the unknown source intensities together with additional auxiliary variables, these latter being defined in such a way as to converge to the solution's process window at the optimum. The objective function is then defined as a function that has the same maximum as the process window when the inputs achieve their optimal values. The core computational step in these conventional methods involves the solution of a linear programming (LP) problem, and their success derives in part from mathematical steps that allow converting certain lithographically important source design problems into near-LP form.
However, LP problems involve continuous variables, and it is only in specialized cases that an LP formulation can successfully optimize over a discrete set of possibilities, or over a discrete set of outcomes (e.g., conditional or contingent parameters). As a result, there are many source optimization problems that the conventional LP-based methods cannot easily handle.
For example, custom diffractive optical elements (DOEs) are currently a preferred method for physically realizing the optimized source solutions provided by the conventional methods. Unfortunately, DOEs are somewhat costly, and require appreciable lead times to obtain. These drawbacks are relatively minor in already-established mass-production processes, particularly those used for high volume ICs. However, DOE cost becomes a larger concern in limited-volume applications. In addition, DOE procurement delays can have a multiplicative impact on cost during process development, particularly when cutting edge lithography is used. This is because process development for advanced lithography requires that experimental calibrations be carried out, and the results of these calibrations can prompt adjustments in the source solution, giving rise to a cyclic process of model iteration. The overall impact can be quite costly if DOE procurement delays arise in each such iteration.
Lithographic exposure tools generally offer limited means for making quick adjustments in the illumination source. Specifically, such tools can usually provide sources of circular or annular shape, whose radii can be adjusted freely over a continuous range. In many cases dipole or quadrupole sources can alternatively be selected, with the location and size of the poles being adjustable to some degree. Moreover, multipart-scans can be used to create sources with shapes that combine more than one of these feature types (e.g., so-called windmill sources, which consist of a disk-shaped central lobe combined with 4 flanking lobes from a quadrupole).
To form a multipart-scan source (multiscan or multipart for short), the exposure tool is commanded to expose each wafer more than once, using a series of supported source shapes in order to produce a total source as a combination of supported source shapes. Unlike other multiple-exposure techniques, a multiscan source does not involve use of multiple masks; instead, multiple scans of a single mask are made in order to build up a complex source by superposition. The relative intensity of the different source components in a multiscan source can be adjusted by varying the dose applied during each part of the scan. The wafer does not have to be re-chucked or re-aligned between scans, and the delays arising from use of multiple scans can often be considered acceptable, particularly in the developmental or low-volume applications that precede use of DOEs. (Once the final process is established, the multiscan source can be recreated as a DOE source of identical shape.) Nonetheless, it is often desirable to limit the number of scans in a multiscan to a reasonably small value, such as 2 or 3.
While the multi-scan technique provides access to a large number of potential source shapes, it does not allow the fully general source shape that the prior-art LP methods generally provide. This is because certain properties of the multi-scan sources are only selectable by choosing from among a discrete set of options (e.g., annulus, dipole, quadrupole, etc.). As a result it is not possible to use the simple bitmap source specification. Other source properties that can be adjusted with the multi-scan technique would ordinarily be considered as parametric adjustments, e.g., adjusting the radii of the annular element of a multi-scan source. However, these parametric adjustments can be approximately recast as discrete options by considering a large number of discrete sources whose parametric setpoints are finely stepped, e.g., a set of annuli having all possible combinations of radii from the set (0, 1/10, 2/10, . . . 1).
To expand upon this point, the solutions provided by the conventional LP method usually take a nominally different form, e.g., a non-parametric form, which more specifically is a list of intensity values that are to be applied to each of a number of continuously adjustable directional pixels to form the source. Usually these pixels are chosen to cover the full extent of the addressable pupil space. These pixels can alternatively be given a non-contiguous or overlapped form; however, even if every source option that is accessible via the multi-scan method were used as a pixel, the LP solution would typically involve use of an impractically large number of such sources.
One problem of a contingent aspect of the above procedure is that when defining a source pixel set that consists of different versions of a standard source under a closely spaced sampling of the parametric source adjustments, there is a requirement that a given pixel in the set can only be switched on if sufficiently many of the remaining pixels (source choices) are switched off. What is needed is a reformulation of the parametric optimization problem as an optimization problem with contingent constraints that can be carried out in a broad range of lithography applications.
A related shortcoming in the conventional methods for intensively customizing sources involves experimentally calibrating the lithographic process models used for optical proximity correction (OPC). Specifically, the prior art lacks good methods for addressing the difficulties imposed by delays in carrying out such calibrations due to a lack of immediate access to the source shape that the optimum DOE provides (these DOEs being subject to long procurement lead times). This difficulty is mitigated by the rough separability that current empirically calibrated process models provide. A process model that is calibrated with conventional (or multi-scan) sources will give approximately correct predictions when provided with the optical inputs that would ultimately be obtained from a planned DOE when it becomes available. However, complete separability is difficult to obtain with current empirical process models, and the DOE source may have a noticeably different shape from all immediately available sources.
It would be desirable to obtain conventional or multi-scan sources that create images which match as closely as possible the images that a planned DOE will provide. Conventional methods do not address this need.
Conventional source optimizations are also not especially well-suited to handle certain constraints on minimum pole size. This is particularly true when avoiding small poles in order to prevent strong spatial coherence effects. Increases in spatial coherence extend the range of non-negligible optical interactions between the images of different features, increasing the computation that is required during each iteration of OPC, and slowing down OPC convergence (e.g., increasing the number of iterations required).
Conventional methods can impose a modest limit on spatial coherence by prohibiting any single source pixel from containing a significant fraction of the total source intensity. Such constraints also suffice to prevent illuminator damage from an overly large concentration of light, in most cases. However, the preferred pole-size constraints are sometimes non-local in the sense that they actually allow source pixels to contain somewhat larger intensity when neighboring source pixels also contain intensity; e.g., sometimes stronger limits may be imposed on the intensity of pixels that are isolated. Source pixels that are large enough to substantially overlap can be used, thereby preventing the source solution from containing overly small isolated poles. (In some cases this construction must be supplemented by finely spaced constraints on the total intensity in regions where pixels overlap.) However, small poles are not problematic if their intensity is low, and the finer pupil resolution they provide can be advantageous. For this reason it is not entirely satisfactory to control pole size by using large overlapped pixels.
Conventional methods can also have difficulty handling a size restriction of another kind, namely one that can arise in customizing the polarization of the source. Sources containing pixels that are exactly overlapped may be optimized, and where each overlapped pixel is identical except for being differently polarized, thus allowing polarization to be selected from among a number of possible choices. However, if the solution provided by this prior-art method should happen to contain non-zero intensity in two or more of the fully overlapped pixels of different polarization, it will be necessary for the illuminator to physically realize the solution by providing partially polarized light in the pixel, which would often be too complicated to arrange, and so would likely force the optimizer to be re-run with a fixed polarization choice in the pixel.
Moreover, practical engineering limitations will often only allow polarization to be varied over pupil-domain scale-lengths that are much coarser than the pixel-scale over which intensity can be controlled. For example, in order to handle the intense deep UV fluences required in high-throughput exposure tools, illumination polarization might typically be controlled using damage-resistant polarizing beamsplitters and stressed-SiO2 retarders. It is not easy to deploy and adjust an array of such components at the fine scale of the source pixels, given that the source pixels will generally be laid out at a density appropriate to the desired fine control of source intensity (e.g., typically at least 50 or more pixels in each pupil quadrant). Instead, it would often be more practical to require, for example, that all pixels in each quarter-section of the pupil share a common polarization, so that they can share a common polarizing beamsplitter.
In terms of an optimized source containing overlapped pixels that represent different polarization choices, it would therefore be desirable to add contingent constraints specifying that an overlapped pixel of a given polarization can only be selected if none of its differently-polarized neighbors in the pupil quarter-section are also switched on. The prior art does not address this need.
The conventional optimization method does not fully reduce most source optimization problems to pure linear programs. Typically the final problems it formulates are decompositions in which one or two nonlinear variables are optimized in an outer loop that iteratively calls an LP solver. Though the solution is typically convex in the nonlinear variables, the need to embed the LP solver (a relatively standard piece of software) in a more complex algorithm is a disadvantage to the conventional global methods. The maximum focal extent used in process window integration is an example of such a nonlinear variable. See further: “Global Optimization of the Illumination Distribution to Maximize Integrated Process Window,” and U.S. Pat. No. 7,057,709.
In many applications source optimization is intended as one step of a larger litho engineering effort involving mask design (e.g., SMO optimization, or RET selection, or OPC). In such cases the most appropriate goal for the source optimization step may not literally be to select the purely optimal source. For example, the particular source which optimizes integrated common process window amongst many features will typically include a number of (usually weakly lit) pixels which essentially serve the role of biasing the intensities at all feature edges in such a way as to align their individual process windows to a common dose threshold. If the mask design is reasonably suitable, these balancing pixels will have low intensity, and a somewhat equivalent effect that can be obtained by small bias adjustments in the mask features (e.g., by OPC adjustment of the fragmented mask feature edges). However, in some cases the local mask bias adjustment will be able to scale the intensity in the region up or down in a way that does not impact contrast as severely as does the best intensity adjustment that the source can provide.
In general, a better performing solution will typically be obtained if the mask and source variables are adjusted jointly. This may requires a separate module for joint local optimization of mask and source together. Alternatively, such applications may be addressed by alternating steps of source and mask optimization, using simple local process-window OPC for the mask step. This is particularly appropriate if the required mask adjustments are small. Strategies for improving the convergence of such a process may also be used, such as maximizing the worst-feature's process window under constraints requiring non-zero overlap of the different feature windows. Nonetheless, the need to engage separate modules for mask optimization in order to appropriately carry out source optimization is a drawback of the conventional methodology.
Though engagement of full SMO (optimization of both mask and source) provides advantages that source optimization alone cannot, these advantages are not always important. For example, synergistic interactions between mask and source are smaller in cases where the mask features have already been assigned approximate shapes and dimensions (but which are not considered fully frozen in their CDs); such as if the exact mask dimensions are not directly of interest but are being calculated to make the source optimization more meaningful, or in cases where only small OPC-like fine tuning of the feature dimensions is allowed. In such cases it is inconvenient that the conventional source optimization methods may require separate operation of a mask design code.
Strong design forms can be found for the purpose of lithographic optimization by replacing the fixed bands that ordinarily define acceptable edge placement positions with more flexible pairwise constraints of the kind used in design migration. See F.-L. Heng, M. A. Lavin, J.-F. Lee, D. Ostapko, A. E. Rosenbluth, and N. Seong, “Lithographic Process Window Optimization Under Complex Constraints on Edge Placement,” U.S. Patent Application Publication No. 2005/0177810A1 (2005) and A. E. Rosenbluth, D. Melville, K. Tian, K. Lai, N. Seong, D. Pfeiffer, and M. Colburn, “Global optimization of masks, including film stack design to restore TM contrast in high NA TCC's,” in SPIE v.6520—Optical Microlithography XX, ed. Donis G. Flagello (2007), p. 65200P.
However, the mathematical methods (transformations and specialized variables) that the conventional global methods use to reformulate source optimization as a near linear programming problem rely on the availability of fixed tolerance boundaries along which the image intensity can be sampled to determine the process window. With flexible pairwise constraints the locations of the tolerance boundaries for each feature edge are not fixed; instead they may be contingent on the location of the tolerance boundaries for other edges. As a result the conventional methods for flexible constraints optimization do not yield global source solutions.
During source optimization it would be desirable to have a way of making the various “requirements” that are typically imposed on the printed pattern be conditional on their basic feasibility. There is not always as strong a distinction in real-world engineering between requirements and goals as there is mathematically between constraints and objective in the conventional optimization problem. For example, the conventional methods often enforce the desired polarity of the image by using constraints which specify that the intensity in the interior of dark parts of the image be no brighter than a fraction RDark of the intensity at the edges of the features, and similarly that the interior intensity of bright image regions be no dimmer than a ratio RBright of the edge intensity. One might typically choose, for example, values of 0.3 and 1.5 respectively for RDark and RBright, since such relatively strong image contrast ratios are generally desirable. However, it can sometimes be impossible to achieve a non-zero process window with an image that exhibits such high contrast. Such a failure may happen, for example, during initial steps of an SMO procedure, since SMO can require more than one cycle of optimization over the mask and source before the working solution reaches a generally acceptable quality. In such cases, one might want to adopt more relaxed contrast requirements (such as RDark=0.7, RBright=1.1), under the contingency that no solution can be obtained under more broadly acceptable contrast requirements. In the prior art, this is accomplished by the inconvenient expedient of re-running the optimization.
The conventional method suffers from similar limitations in respect to other constraints—In general terms, it does not provide for contingent selection of the numerical values used to constrain the solution in various respects, unless the user is willing to re-run the optimization when each such contingency is encountered. In such cases the inconvenience of a strategy of repeatedly re-running the optimization can become significant.
Certain conventional methods of SMO are subject to another kind of efficiency limitation when multiple independent regions of a mask are being optimized together. These SMO algorithms include a mask optimization step (which is alternated with source optimization) where the mask design is arrived at implicitly by optimizing the diffraction orders that project through the lens to the wafer, with specific mask features being synthesized during a subsequent “wavefront engineering” step. See further: “Optimum Mask and Source Patterns to Print a Given Shape,”, “Global optimization of masks, including film stack design to restore TM contrast in high NA TCC's,” and A. E. Rosenbluth and J. T. Azpiroz, “Method for Forming Arbitrary Lithographic Wavefronts Using Standard Mask Technology,” U.S. patent application Ser. No. 12/431,865, filed Apr. 29, 2009.
Multiple mask regions can be considered when this kind of SMO is employed. Typically the source optimization step involves finding a single source solution for all parts of the mask, while the different regions of the mask are typically optimized independently (e.g., in their local diffraction orders). When such a mask region is being independently optimized, the exact intensity of the wafer image provided by the diffraction order variables is not generally important, even though the independent mask regions need to eventually be “synchronized” in dose for deployment on a common mask.
The mask optimization problem can be simplified when the absolute intensity level can be neglected, and such is possible when optimizing multiple mask regions because the relative image intensities provided by the different sets of independently optimized diffraction orders need to only be adjusted to match during a later stage of the SMO procedure (namely the wavefront engineering step in which the orders are reduced to specific mask shapes). However, this class of SMO algorithm also includes a source optimization step, in which the source is optimized to print all mask regions simultaneously. This source solution therefore does become dependent on the choice of relative intensity adjustments for the different mask regions, which should be made optimally. Relative intensity adjustment factors may be included as new variables during source optimization. As with the focal range variable described above, the conventional source optimization method optimizes the nonlinear intensity adjustment variables in an outer loop that iteratively calls an LP solver. There is again a disadvantage due to the need to embed the LP solver (a relatively standard piece of software) inside a more complex algorithm.